Per my company Flight Operations Manual:
The phrase “declaring an emergency” no longer appears in FAA Pilot/Controller Glossary or the FAA 7110. The only method appearing in FAA or ICAO guidance is to declare a distress situation is the use of the word “Mayday” repeated three times. Pilots are cautioned that the use of the phrase “declaring an emergency” is not in compliance with regulatory guidance. (Nov 2017)